Answer:
[tex]v = \frac{32\pi}{3}[/tex]
or
[tex]v=33.52[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 4x - x^2[/tex]
[tex]g(x) = x^2[/tex]
[tex][a,b] = [0,2][/tex]
Required
The volume of the solid formed
Rotating about the x-axis.
Using the washer method to calculate the volume, we have:
[tex]\int dv = \int\limit^b_a \pi(f(x)^2 - g(x)^2) dx[/tex]
Integrate
[tex]v = \int\limit^b_a \pi(f(x)^2 - g(x)^2)\ dx[/tex]
[tex]v = \pi \int\limit^b_a (f(x)^2 - g(x)^2)\ dx[/tex]
Substitute values for a, b, f(x) and g(x)
[tex]v = \pi \int\limit^2_0 ((4x - x^2)^2 - (x^2)^2)\ dx[/tex]
Evaluate the exponents
[tex]v = \pi \int\limit^2_0 (16x^2 - 4x^3 - 4x^3 + x^4 - x^4)\ dx[/tex]
Simplify like terms
[tex]v = \pi \int\limit^2_0 (16x^2 - 8x^3 )\ dx[/tex]
Factor out 8
[tex]v = 8\pi \int\limit^2_0 (2x^2 - x^3 )\ dx[/tex]
Integrate
[tex]v = 8\pi [ \frac{2x^{2+1}}{2+1} - \frac{x^{3+1}}{3+1} ]|\limit^2_0[/tex]
[tex]v = 8\pi [ \frac{2x^{3}}{3} - \frac{x^{4}}{4} ]|\limit^2_0[/tex]
Substitute 2 and 0 for x, respectively
[tex]v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ \frac{2*0^{3}}{3} - \frac{0^{4}}{4} ])[/tex]
[tex]v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ 0 - 0])[/tex]
[tex]v = 8\pi [ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ][/tex]
[tex]v = 8\pi [ \frac{16}{3} - \frac{16}{4} ][/tex]
Take LCM
[tex]v = 8\pi [ \frac{16*4- 16 * 3}{12}][/tex]
[tex]v = 8\pi [ \frac{64- 48}{12}][/tex]
[tex]v = 8\pi * \frac{16}{12}[/tex]
Simplify
[tex]v = 8\pi * \frac{4}{3}[/tex]
[tex]v = \frac{32\pi}{3}[/tex]
or
[tex]v=\frac{32}{3} * \frac{22}{7}[/tex]
[tex]v=\frac{32*22}{3*7}[/tex]
[tex]v=\frac{704}{21}[/tex]
[tex]v=33.52[/tex]
Write the equation of the line that passes through the points (7, -3) and (7, 0).
Answer:
x = 7
Step-by-step explanation:
Since the x- coordinates of the 2 points are equal, both 7 , then the line is vertical with equation
x = c
where c is the value of the x- coordinates the line passes through, then
x = 7 ← equation of line
Answer:
I hope this is right, im not sure because they are coincides or the same lines when overlapped, but I tried.
3x+0
Step-by-step explanation:
Using the formula mx+b we can get our answer.
We know that the two points pass through (7, 0)
mx+b is (slope)x+(y-intercept)
The slope of the two lines is 3 so we can replace m for 3:
3x+b
the y-intercept does not exist for these two lines as they are coincides, so we can just put it at 0, so we now have our equation 3x+0.
Find the 67th term of the following arithmetic sequence.
5, 11, 17, 23, ??
Answer:
401
Step-by-step explanation:
a = 5
d = [tex]a_2[/tex] - a
= 11 - 5
= 6
[tex]a_{67}[/tex]= a + (n-1)d
= 5 + (67-1)6
= 5 + 66 × 6
= 5 + 396
= 401
Answer:
401. is your correct answer.
2.The marked price of television is Rs2000.If 13 percentage tax was levied, after allowing 10 percentage discount, find the final price.Single choice.
(2 Points)
Answer:
Final price = $2034
Step-by-step explanation:
Given the following data;
Marked price = $2000
Tax = 13%
Discount = 10%
To find the final sales price;
First of all, we would calculate the discount price
Discount price = 10/100 * 2000
Discount price = 20 * 10 = $200
New Price = marked price - discount price
New Price = 2000 - 200 = 1800
Next, we calculate the tax on the product;
Tax = 13/100 * 1800
Tax = 0.13 * 1800
Tax = $234
Finally, we would determine the final price;
Final price = marked price + Tax
Final price = 1800 + 234
Final price = $2034
In 2002, the manufacturers of M&M's surveyed people from around the world and asked them to vote for a new color: purple, aqua, or pink. In the United States, 42% of those who voted said purple, 37% said aqua, and 19% said pink. What's the probability that a randomly picked survey respondent from the United States preferred purple or pink?
Answer:
don't know
Step-by-step explanation:
dont know...........
INFO: The chairs are evenly spaced around
the wheel
Question: If the length of the cable from L to E is 80 feet, E to the ground is 35 feet, and F to the ground is 40
feet, what is the length of the cable from J to F?
Answer: About 72 feet
The more accurate value is roughly 71.7260397 feet (however, this value isn't fully exact either).
======================================================
Explanation:
Check out the diagram below. It's effectively the same diagram your teacher provided, but I've added points M and N. I've left out any unnecessary lines.
M = center of the circleN = location where the cable is anchored to the groundWe're told that "(the length of cable from) E to the ground is 35 feet", so this is the red portion of cable that I've marked this as NE = 35, ie segment NE is 35 feet long. We're also told that NF = 40 feet, which is also shown in red.
The blue portions are chords of the circle. We're given one chord as LE = 80 ft, while the other chord JF is what we want to find out.
-----------------
What we need to find is the radius of this circle. Right away, it's not clear what the radius is; however, we can use the chord LE = 80 to help find it.
It turns out that the chord length c is connected to the radius r and central angle theta like so:
c = 2*r*sin(0.5*theta)
where theta must be in radian mode. The central angle subtends the arc that forms the chord in question.
If we started at point L, and counted the number of spaces to get to E while going clockwise, then we can see that there are 5 spaces
Those five spaces could be written as
The jump from L to AThe jump from A to BThe jump from B to CThe jump from C to DThe jump from D to EOr you could mark it as such on the diagram for a visual reference. Overall, the circle has been cut into 12 equal slices. So going from L to E, going clockwise, will have us take up 5/12 of the full circle.
There are 2pi radians in a full circle, meaning the central angle LME is (5/12)*2pi = 5pi/6 radians.
-----------------
Plug theta = 5pi/6 and c = 80 into the formula mentioned. Isolate the radius.
c = 2*r*sin(0.5*theta)
80 = 2*r*sin(0.5*5pi/6)
80 = 2*r*sin(5pi/12)
80 = 2*r*0.9659258
80 = 2*0.9659258*r
80 = 1.9318516r
1.9318516r = 80
r = 80/1.931 8516
r = 41.4110483
The radius is approximate. The radius is in feet. Make sure your calculator is in radian mode.
-----------------
Now that we know the radius, we can determine how long chord JF is.
The central angle for chord JF is angle JMF
If we start at J and go to F, along the shorter path, then we've gone 4 spaces. This is 4/12 = 1/3 of the full circle. So the radian measure of angle JMF is (1/3)*2pi = 2pi/3 radians.
So,
c = 2*r*sin(0.5*theta)
c = 2*41.4110483*sin(0.5*2pi/3)
c = 71.7260397
Chord JF is roughly 71.7260397 feet long.
When rounding to the nearest foot, that's about 72 feet.
A cylinder has no lateral faces.
a. true
b. false
Answer: it’s a
Step-by-step explanation:
there are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
To the nearest inch, how many inches are in 14 meters?
Answer:
551
Step-by-step explanation:
Answer:
551.18 inches
Step-by-step explanation:
convert 14 m to cm, so multiply 14 by 100, to get 1400, then convert to inches, so divide by 2.54, which gives you 551.18 inches
I need help please ASAP
H. 200 miles in 4 hours
represents a constant rate of change of 50 miles per hour.
Answer:
H. 200 miles in 4 hours.
Step-by-step explanation:
200 miles in 4 hours.
In this situation, in 4 hours, the vehicle has driven a distance of 200 miles.
To determine the distance in one hour, divide the miles by the hour.
200 ÷ 4 = 50.
The vehicle drives at a constant rate of 50 miles per hour.
HELP ME !! AND EXPLAIN HOW YOU GOT IT.
PLEASE ANSWER !! ILL GIVE BRAINLIEST !!
50 POINTS !!
FAKE ANSWERS WILL GET REPORTED .
Answer:
<1= 62
•it is 62 because it is an alternate interior angle which is congruent
<2= 83
• when you add the given angles 62 and 35 you get 97 and a triangle is 180 so you subtract 97 from 180
<3=35
• it is 35 because it is an alternate interior angle which is congruent
Step-by-step explanation:
62+35= 97
180-97= 83
Drag the tiles to match each measurement with an equivalent measurement.
8 quarts 1 cup 1 gallon 12 cups
Measurement Equivalent Measurement
6 pints
16 pints
8 fluid ounces
8 pints
Answer:
Measurement Equivalent Measurement
6 pints 12 cups
16 pints 8 quarts
8 fluid ounces 1 cup
8 pints 1 gallon
Step-by-step explanation:
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 fluid ounces
Measurement Equivalent Measurement
6 pints 12 cups
16 pints 8 quarts
8 fluid ounces 1 cup
8 pints 1 gallon
A report about how American college students manage their finances includes data from a survey of college students. Each person in a representative sample of 793 college students was asked if they had one or more credit cards and if so, whether they paid their balance in full each month. There were 500 who paid in full each month. For this sample of 500 students, the sample mean credit card balance was reported to be $825. The sample standard deviation of the credit card balances for these 500 students was not reported, but for purposes of this exercise, suppose that it was $195. Is there convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $907, the value reported for all college students with credit cards?
Required:
a. Carry out a hypothesis test using& significance level of 0.01.
b. State the appropriate null and alternative hypotheses.
Answer:
Following are the responses to the given question:
Step-by-step explanation:
Test statistic:
[tex]t=\frac{(825-905)}{\frac{205}{\sqrt{(500)}}}[/tex]
[tex]=\frac{(-80)}{\frac{205}{22.36}}\\\\=\frac{(-80)}{9.16}\\\\=-8.73[/tex]
Let the p-value=0
We reject H0 because of the p-value <0.01. We have evidence that college kids who pay their credit card bills in full per month have a mean balance of less than $905.
For the following hypothesis test, determine the null and alternative hypotheses. Also, classify the hypothesis test as two-tailed, left-tailed, or right-tailed. The mean length of imprisonment for motor-vehicle theft offenders in this country is 22.1 months. A hypothesis test is to be performed to determine whether the mean length of imprisonment for motor-vehicle theft offenders in this city differs from the national mean of 22.1 months.
Choose the correct null and alternative hypotheses below.
A. H0: μ = 22.1 months
Ha: μ > 22.1 months
B. H0: μ = 22.1 months
Ha: μ 22.1 months
C. H0: μ = 22.1 months
Ha: μ < 22.1 months
D. H0: μ > 22.1 months
Ha: μ = 22.1 months
E. H0: μ 22.1 months
Ha: μ = 22.1 months
F. H0: μ = 22.1 months
Ha: μ > 22.1 months
Which of the following is the correct classification of the hypothesis test?
A. Two-tailed
B. Left-tailed
C. Right-tailed
Answer:
Option B:
[tex]H_0: \mu = 22.1[/tex]
[tex]H_a: \mu \neq 22.1[/tex]
Classification:
The hypothesis test is Two-tailed.
Step-by-step explanation:
The mean length of imprisonment for motor-vehicle theft offenders in this country is 22.1 months.
This means that the null hypothesis is that the mean is of 22.1 months, that is:
[tex]H_0: \mu = 22.1[/tex]
A hypothesis test is to be performed to determine whether the mean length of imprisonment for motor-vehicle theft offenders in this city differs from the national mean of 22.1 months.
At the alternate hypothesis, we test if this mean is different of 22.1, that is:
[tex]H_a: \mu \neq 22.1[/tex]
Which means that the answer is given by option b).
Which of the following is the correct classification of the hypothesis test?
We test if the mean is different from a value, which means that the hypothesis test is Two-tailed.
Which angle is supplementary to CFD?
Answer:
∠DFA or can be written as AFD : ( as long as the vertex F is in the middle)
Step-by-step explanation:
Supplementary angles are angles when added together form a straight line (180°)
CFD makes a small part of that straight line and DFA (AFD) make up the other part
FOUR balls are selected from a bag containing 15 red and 5 blue balls. What is the probability that:
(a) exactly 3 are red if the balls are replaced each time?
(b) exactly 3 are red if the balls are not replaced?
Which angles are adjacent to DFE?
Select all that apply.
9514 1404 393
Answer:
(c) ∠BFD
Step-by-step explanation:
Angle DFE is created from rays FD and FE. An adjacent angle will have one of those rays as one of its sides. Of the offered choices, only ∠BFD includes one of those two rays as one of its sides.
HELP ME PLEASEEEEEEEEEEE
Answer: -5,1
Step-by-step explanation: Hope this help :D
Find the area of the shaded region:
Answer:
34560
Step-by-step explanation:
You have to multiply to get your answer
Hope I'm right...
Hope this helps plz like and brainly :D
what is the solution
Answer:
y
≥
14
Step-by-step explanation:
There are ten shirts in your closet, four blue and six green. You randomly select one to wear on Monday and then a different one on Tuesday. You wear a blue shirt on Monday and a green shirt on Tuesday
this is very simple. so basically u need statistic for the persetage of finding the answer. basically what jm saying is if u wear a blue shirt on monday and green on tuesday. then thertiocially u should wear a opsiote the following week. hope rhis helps :)
Emilio is drawing a graph that shows the weight of a baby elephant during the first 6 months of its life. What is the meaning of the point shown on the graph?
Ruby's Weight
A graph has age (months) on the x-axis, and weight (pounds) on the y-axis. A point is at (1, 80).
Using the function concept, it is found that the meaning of the point is that the weight of the elephant during the first month is of 80 pounds.
What is a function?In a function, represented by a set of ordered points (x,y), one value of the input x can be related to only one value of the output y.
In this problem, x is the age in months, while y is the weight in pounds, hence the meaning of point (1,80) is that the weight of the elephant during the first month is of 80 pounds.
More can be learned about the function concept at https://brainly.com/question/12463448
What is the median of the following data values?
108, 102, 43, 100, 22
O A. 80
O B. 95
O C. 100
O D. 75
Answer:
100
Step-by-step explanation:
You're correct :) good job
A jar contains 21 brown and 19 blue marbles. A marble is drawn at random. What is the theoretical probability of drawing a blue marble? P(blue) = 63.3% P(blue) = 47.5% P(blue) = 2.5% P(blue) = 19% P(blue) = 52.5%
Answer:
The answer would be the 1st one.
Step-by-step explanation:
When you use a percentage calculator or look it up, you can shay 40 as a percent of 19 and the answer will be 47.5%. You could also divide and get your answer that way as well.
Hope that helps! If you get it wrong, please tell me so I could check my work. Have a great rest of your day :)!
PLEASE HELP ME WITH THIS :<
Answer:
i think its the third one correct me if im wrong 0:)
Answer:
it should be the 3rd one
Yousef buys 40 tokens at the carnival. He gives his sister tokens for 5 kiddie rides. He wants to use the remaining token for thrill rides for himselt.
thrill rides use 5 tokens each and kiddie rides use 3 tokens each, what is the largest number of thrill rides Yousef can go on?
Answer:
5 rides
Step-by-step explanation: Multiply the number of kiddie rides his sister will go on (5) by the amount of tickets it costs each (3). subract that from 40 (the initial amount of tickets). then divide that by 5 (amount of tickets for 1 thrill ride)
4. Sharlene walked 7 2/11
km to school an 2 8/11
km to the park. How many
Kilometers dild she walk in all
Answer:
9 10/11 km
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
7 2/11 km to school
Another 2 8/11 km to the park
Step 2: Find Total
Add: 9 10/11 kmSally has 2 pets in her house. The weight of her dog is 50 pounds and the weight of her cat is 12 pounds. By how much is the weight of the dog more than the weight of the cat?
A. 38 lb.
B. 30 lb.
C. 28 lb.
D. 20 lb.
Answer:
the answer is A. 38lb.
i hope this helps :)
Step-by-step explanation:
Which of the following is equivalent to ^5sqrt13^3
Answer:
The last one 13^3/5
Step-by-step explanation:
13^3/5
Members of a basketball team are reviewing their scores from the last several games. They record their point totals in the stem-and-leaf plot shown.
Use the drop-down menu below to answer the question about the stem-and-leaf plot.
Answer:
13 games
Step-by-step explanation:
Answer:
13 games
Step-by-step explanation:
the values at which the graph of polynomial crosses the _-axis are called "roots" and are the values for which the y-value is zero.
Answer:
x- axisStep-by-step explanation:
The blank is the x-axis
2. Two puppies together weigh 22 kilograms 300 grams. If one
puppy weighs 9 kilograms 500 grams, how heavy is the other
puppy?
Tip: 1 kg = 1000 g
answer asap
Answer:
B = 12800 grams or 12kg 800 grams.
Step-by-step explanation:
Let the two puppies be A and B respectively.
Translating the word problem into an algebraic expression, we have;
A + B = 22kg 300g
A = 9kg 500g
Conversion;
1 Kilograms = 1000 grams.
9kg 500g = 9*1000 + 500 = 9500 grams
22kg 300g = 22*1000 + 300 = 22300 g
Substituting into the above formula, we have;
9500 + B = 22300
B = 22300 - 9500
B = 12800 grams or 12kg 800 grams